R. Hiyya b. Abba fell ill and R. Johanan went in to visit him. He said to him: Are your sufferings welcome to you? He replied: Neither they nor their reward. He said to him: Give me your hand. He gave him his hand and he raised him. R. Johanan once fell ill and R. Hanina went in to visit him. He said to him: Are your sufferings welcome to you? He replied: Neither they nor their reward. He said to him: Give me your hand. He gave him his hand and he raised him. Why could not R. Johanan raise himself? - They replied: The prisoner cannot free himself from jail. -Talmud, Berachot 5b
R. Helbo is sick. But none visited him. He rebuked them [sc. the scholars], saying, 'Did it not once happen that one of R. Akiba's disciples fell sick, and the Sages did not visit him? So R. Akiba himself entered [his house] to visit him, and because they swept and sprinkled the ground before him,he recovered. 'My master,' said he, 'you have revived me!' [Straightway] R. Akiba went forth and lectured: He who does not visit the sick is like a shedder of blood. -Talmud, Nedarim 40a
He who visits the sick causes him to live, whilst he who does not causes him to die. -Talmud, Nedarim 40a
Rab said: He who visits the sick will be delivered from the punishments of Gehenna, for it is written, Blessed is he that considereth the poor: the Lord will deliver him in the day of evil. 'The poor' [dal] means none but the sick, as it is written, He will cut me off from pining sickness [mi-dalah]. -Talmud, Nedarim 40a
R. Shisha son of R. Idi said: One should not visit the sick during the first three or the last three hours [of the day], lest he thereby omit to pray for him. During the first three hours of the day his [the invalid's] illness is alleviated; in the last three hours his sickness is most virulent. -Talmud, Nedarim 40a
R. Abba son of R. Hanina said: He who visits the sick takes away a sixtieth of his pain. -Talmud, Nedarim 39b
We have to not only take care of ourselves; we also have to take care of each other. We all have moments when we need to depend on others for our well being, and we all have the opportunity to be a help to those who have helped us. The sages of the Talmud went into great detail regarding why one should visit the sick, when you should visit, and how you can best be a help and not a hindrance. The mitzvah (commandment) of visiting the sick is one of those that brings out the best in humanity.